2020-12-09T15:44:10Z
Acceptance in OA@INAF
HST/STIS analysis of the first main sequence pulsar CU Virginis
Title
þÿKrtika, J.; Mikuláaek, Z.; Henry, G. W.; Janík, J.; Kochukhov, O.; et al.
Authors
10.1051/0004-6361/201834937
DOI
http://hdl.handle.net/20.500.12386/28755
Handle
ASTRONOMY & ASTROPHYSICS
Journal
625
arXiv:1903.07331v1 [astro-ph.SR] 18 Mar 2019
March 19, 2019
HST/STIS analysis of the first main sequence pulsar CU Vir
⋆
J. Krtiˇcka
1, Z. Mikulášek
1, G. W. Henry
2, J. Janík
1, O. Kochukhov
3, A. Pigulski
4, P. Leto
5, C. Trigilio
5, I. Krtiˇcková
1,
T. Lüftinger
6, M. Prvák
1, and A. Tichý
11 Department of Theoretical Physics and Astrophysics, Masaryk University, Kotláˇrská 2, CZ-611 37 Brno, Czech Republic
2 Center of Excellence in Information Systems, Tennessee State University, Nashville, Tennessee, USA
3 Department of Physics and Astronomy, Uppsala University, Box 516, 751 20, Uppsala, Sweden
4 Astronomical Institute, Wrocław University, Kopernika 11, 51-622, Wrocław, Poland
5 INAF – Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy
6 Institut für Astronomie, Universität Wien, Türkenschanzstraße 17, 1180 Wien, Austria
Received
ABSTRACT
Context.CU Vir has been the first main sequence star that showed regular radio pulses that persist for decades, resembling the radio lighthouse of pulsars and interpreted as auroral radio emission similar to that found in planets. The star belongs to a rare group of magnetic chemically peculiar stars with variable rotational period.
Aims.We study the ultraviolet (UV) spectrum of CU Vir obtained using STIS spectrograph onboard the Hubble Space Telescope (HST) to search for the source of radio emission and to test the model of the rotational period evolution.
Methods. We used our own far-UV and visual photometric observations supplemented with the archival data to improve the pa-rameters of the quasisinusoidal long-term variations of the rotational period. We predict the flux variations of CU Vir from surface abundance maps and compare these variations with UV flux distribution. We searched for wind, auroral, and interstellar lines in the spectra.
Results.The UV and visual light curves display the same long-term period variations supporting their common origin. New updated abundance maps provide better agreement with the observed flux distribution. The upper limit of the wind mass-loss rate is about
10−12M
⊙yr−1. We do not find any auroral lines. We find rotationally modulated variability of interstellar lines, which is most likely
of instrumental origin.
Conclusions.Our analysis supports the flux redistribution from far-UV to near-UV and visual domains originating in surface abun-dance spots as the main cause of the flux variability in chemically peculiar stars. Therefore, UV and optical variations are related and the structures leading to these variations are rigidly confined to the stellar surface. The radio emission of CU Vir is most likely powered by a very weak presumably purely metallic wind, which leaves no imprint in spectra.
Key words. stars: chemically peculiar – stars: early type – stars: variables – stars: individual CU Vir
1. Introduction
The magnetic chemically peculiar star CU Virginis (HR 5313, HD 124224) is one of the most enigmatic stars of the upper part of the main sequence. CU Vir shows continuum radio emis-sion, explained as due to gyrosynchrotron process from electrons spiraling in a co-rotating magnetosphere. According to Leto et al. (2006), a stellar wind with mass-loss rate on the order of 10−12M
⊙yr−1is a source of free electrons. But the most intrigu-ing behavior of CU Vir is the presence of a coherent, highly di-rective radio emission at 1.4 GHz, at particular rotational phases, interpreted as electron cyclotron maser emission (Trigilio et al. 2000; Ravi et al. 2010; Lo et al. 2012). In this interpretation, CU Vir is similar to a pulsar, even if the emission process is different, resembling auroral activity in Earth and major plan-ets (Trigilio et al. 2011). This type of emission is not unique among hot stars, as evidenced by the detection of electron cy-clotron maser emission from other magnetic chemically peculiar
⋆ Based on observations made with the NASA/ESA Hubble Space
Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are asso-ciated with program #14737.
stars (Das et al. 2018; Lenc et al. 2018; Leto et al. 2019). The au-roral radio emission from stars with a dipole-like magnetic field has been modeled by Leto et al. (2016). This opens a new the-oretical approach to the study of the stellar auroral radio emis-sion and, in particular, this method could be used to identify the possible signature of a star-planet magnetic interaction (like the Io-Jupiter interaction, Hess & Zarka 2011; Leto et al. 2017).
However, a star with parameters that correspond to CU Vir is not expected to have a stellar wind required to explain the observed continuum radio emission (Krtiˇcka 2014). Moreover, weak winds are subject to decoupling of metals (Owocki & Puls 2002; Krtiˇcka & Kubát 2002; Votruba et al. 2007), which has not yet been observationally verified. Consequently, the detection of “auroral” utraviolet (UV) lines is desirable to further support to the current model of pulsed radio emission.
CU Vir belongs to the group of hot magnetic chemically peculiar stars. These hot stars are usually slowly rotating, and possess notable outer envelopes mostly without convective and meridional motions. This allows the radiatively driven diffusion to be effective, and with occurrence of a global (possibly fos-sil) magnetic field, it may give rise to the chemical peculiarity and consequently to persistent surface structures (Michaud 2004; Alecian et al. 2011). These structures manifest themselves in
a periodic spectrum and spectral energy distribution variability, frequently accompanied by variations of the effective magnetic field (Kuschnig et al. 1999; Lüftinger et al. 2010; Kochukhov et al. 2014). The persistent surface structures (spots) differ from transient dark solar-type spots that originate due to the suppres-sion of convective motion in the regions with enhanced local magnetic field and last for short time scales only.
The detailed nature of the rotationally modulated light vari-ability of chemically peculiar stars remained elusive for decades. The problem became clearer after application of advanced stel-lar model atmospheres calculated assuming elemental surface distributions derived from surface Doppler mapping based on optical spectroscopy. This enabled us to construct photomet-ric surface maps and to predict light variability (e.g., Krtiˇcka et al. 2012; Prvák et al. 2015). The result supports the current paradigm for the nature of the light variability of chemically pe-culiar stars, according to which this light variability is caused by the redistribution of the flux from the far-UV to near-UV and visible regions due to the bound-bound (lines, mainly iron or chromium, Kodaira 1973; Molnar 1973) and bound-free (ioniza-tion, mainly silicon and helium, Peterson 1970; Lanz et al. 1996) transitions, the inhomogeneous surface distribution of elements, and modulated by the stellar rotation. However, in CU Vir this model is not able to explain fully the observed UV and optical light variability (Krtiˇcka et al. 2012), particularly in the Ström-gren u color and around 1600 Å in the UV domain.
Moreover, being an unusually fast rotator, CU Vir belongs to a rare group of magnetic chemically peculiar stars that show secular variations of the rotation period (Pyper et al. 1998, 2013; Mikulášek et al. 2011; Mikulášek 2016). These variations were interpreted as a result of torsional oscillations (Krtiˇcka et al. 2017), which stem from the interaction of an internal magnetic field and differential rotation (Mestel & Weiss 1987). The varia-tions were not, however, directly detected in the UV domain.
All these open problems connected with the atmosphere, magnetosphere, and wind of CU Vir can be adequately addressed by dedicated high-resolution UV observations. Here we describe our HST/STIS observations aiming to get a more detailed picture of the CU Vir UV light variability and its magnetosphere.
2. Observations
2.1. HST and IUE ultraviolet observations
Our HST observations were collected within the program #14737 using the STIS spectrograph with 31X0.05NDA slit, E140H grating in positions corresponding to the central wave-lengths 1380 Å and 1598 Å, and using the FUV-MAMA detector. The observations are homogeneously distributed over CU Vir ro-tational phase and cover the wavelength regions 1280 – 1475 Å and 1494 – 1688 Å (see Table 1). The observations were pro-cessed via standard STIS pipelines and were downloaded from the MAST archive. We further applied the median filter to reduce the noise in the spectra.
Observations from the HST nicely cover the rotation cy-cle of the star (see Fig. 1). The observations close to the phase ϕ ≈ 0 correspond to visual minimum and to UV maxi-mum. This is also the phase of the start of XMM-Newton X-ray observation (ϕ ≈ 0.07, Robrade et al. 2018). The spectra od5y02010 and od5y02020 correspond to the period of X-ray quiescence roughly 7 ks after the start of observation. The spec-trum od5y03010 was obtained close to the a peak of radio emis-sion, which is observed around the phases 0.29 − 0.35 (Trigilio et al. 2008). This is also approximately the period of maximum
Table 1.HST/STIS observations of CU Vir.
Spectrum Region [Å] HJDmean mean phase
od5y02010 1380 2 457 948.6933 0.220 od5y02020 1598 2 457 948.7062 0.245 od5y03010 1380 2 457 945.6472 0.370 od5y03020 1598 2 457 945.6602 0.395 od5y04010 1380 2 457 953.5934 0.631 od5y04020 1598 2 457 953.6067 0.657 od5y05010 1380 2 457 947.4351 0.804 od5y05020 1598 2 457 947.4480 0.828 od5y51010 1380 2 458 254.2392 0.036 od5y51020 1598 2 458 254.2522 0.061
Notes.The phases ϕ were calculated according to the ephemeris Eq. (4).
rotational phase -0.2 0 0.2 0.4 0.6 0.8 1 1.2 ∆ m [mag] -0.5 0 0.5 1 1.5 2 2.5 3 130 135 140 152.5 155 630
Fig. 1.Comparison of light curves in far UV and red regions of CU Vir
spectrum. Blue circles and red squares denote synthetic magnitudes de-rived from IUE and STIS spectra and lilac points are the measurements from SMEI satellite. Wavelengths are expressed in nanometers. Phases are calculated using ephemeris Eq. (4) applying parameters given in Ta-ble 2. Green lines are the fits of the light curve phenomenological model Eq. (3), assuming two photometric spots with photocenters at the phases 0.303 and 0.598 (denoted using vertical black dotted lines). Light curves were plotted relative to the mean value of the fits and vertically shifted to separate individual plots.
strength of Si lines, which appears roughly around the phase ϕ ≈ 0.35 (Kuschnig et al. 1999) and which corresponds to strong X-ray flux roughly 15 ks after the start of XMM-Newton obser-vations. The maximum strength of Fe lines and optical maxi-mum is observed slightly later around the phase 0.5. The spec-trum od5y04020 marks the end of XMM-Newton observations.
The peak b of radio emission is located around ϕ = 0.71 − 0.77, close to which the spectrum od5y05010 was obtained. This also roughly marks the start of Chandra observations (ϕ = 0.76). These observations end at ϕ = 0.40.
We supplemented the HST CU Vir observations with IUE data (PI: M. Maitzen, see Sokolov 2000; Krtiˇcka et al. 2012, hereafter Paper I). To obtain the UV photometry, we extracted IUE observations of CU Vir from the INES database using the SPLAT package (Draper 2004, see also Škoda 2008). We down-loaded low-dispersion data originating from high-dispersion large aperture spectra in the domains 1250–1900 Å (SWP cam-era) and 2000–3000 Å (LWR camcam-era). For the spectroscopic analysis, we used high-dispersion IUE data downloaded from the MAST archive. We compared the absolute flux normalization of HST and IUE spectra concluding that these flux normalizations are consistent (within small differences which can be attributed to calibration).
We used the HST and IUE SWP fluxes F(λ) to calculate UV magnitudes (see Fig. 1)
mc= −2.5 log "Z ∞ 0 Φc(λ)F(λ) dλ # , (1) where Φc(λ) = √ πσ−1exp−(λ − c)2/σ2 is a normalized Gauss function centered on the wavelength c. The central wave-lengths of individual Gauss filters cover HST spectra, c = 1300 Å, 1350 Å, 1400 Å, 1525 Å, and 1550 Å. The dispersion was selected σ = 10 Å for c = 1300 Å and 1525 Å, and σ = 25 Å for the remaining ones. Figure 1 shows that the IUE and HST light curves are very similar with small differences most likely due to instrumental calibration.
We derived the synthetic photometry from IUE LWR spectra also using Eq. (1) (see Mikulášek et al. 2011). The UV synthetic photometry of HST and IUE was further supplemented by the data derived from OAO II satellite (Molnar & Wu 1978). 2.2. Standard photometry
In addition to the 326 photometric measurements derived from the UV spectra taken by HST and IUE and adopted from Molnar & Wu (1978), we also used 35 803 other available photometric data obtained in the time interval 1972 – 2018 by various ob-servers in the region 330–753 nm using standard photometric techniques (see Mikulášek 2016, for the list). We supplemented these data with two additional sets of observations.
From 2010 February through 2018 June, we acquired 1191 photometric observations in the Johnson V band and 1327 in the Johnson B band, with Tennessee State University’s T3 0.40 m automatic photoelectric telescope (APT) at Fairborn Observa-tory in the Patagonia Mountains of southern Arizona (Henry 1999). Each observation in each filter represents the mean of three differential measurements of CU Vir bracketed by four measurements of its comparison star HD 125181. Details on the acquisition and reduction of the observations can be found in our paper on HR 7224 (Krtiˇcka et al. 2009).
The space photometry of CU Vir is available from the So-lar Mass Ejection Imager (SMEI) experiment (Eyles et al. 2003; Jackson et al. 2004). The experiment was placed on-board the Coriolis spacecraft and aimed to measure sunlight scattered by free electrons of the solar wind. A by-product of the mission is the photometry of bright stars all over the sky, available through the University of California San Diego (UCSD) web page1. The
1 http://smei.ucsd.edu/new_smei/index.html
SMEI passband covers the range between 450 and 950 nm (Eyles et al. 2003). The photometry of stars was obtained using a tech-nique developed by Hick et al. (2007). The SMEI stellar time series are affected by long-term calibration effects, especially a repeatable variability with a period of one year. They also re-tain unwanted signals from high energy particle hits and aurorae. Nevertheless, the SMEI observations are well suited for study-ing variability of bright stars primarily because they cover an extended interval – 2003 to 2010.
The raw SMEI UCSD photometry of CU Vir was first cor-rected for the one-year variability by subtracting an interpolated mean light curve. This curve was obtained by folding the raw data with the period of one year, calculating median values in 200 intervals in phase, and then interpolating between them. In addition, the worst parts of the light curve and outliers were re-moved. Then, a model consisting of the sinusoid with rotational frequency of CU Vir and its detectable harmonics was fitted to the data. The low-frequency instrumental variability was filtered out by subtracting trends that were calculated using residuals of the fit and removing outliers using σ-clipping. The trends were approximated by calculating averages in time intervals which were subsequently interpolated. The final SMEI light curve con-sists of 19 226 individual data points.
2.3. Optical spectroscopy
Additional optical spectra were obtained at Astronomical obser-vatory in Piwnice (Poland). We used a mid-resolution echèlle spectrograph (R ∼ 15 000) connected via optical fiber to the 90 cm diameter Schmidt-Cassegrain telescope. Spectra were ob-served during two weekly runs in 2010 (March 3 – 10, April 4 – 8) and during one night in 2011 (February 10). Th-Ar calibration spectrum was taken before and after each scientific image. For reduction we used standard IRAF2routines (bias, flat, and wave-length calibration). In total we collected 59 spectra, which cover wavelength regions from 4350 –7160 Å and all rotational phases of the star.
3. Long-term rotational period variations
The method used to monitor CU Vir long-term rotational period variations is based on the phenomenological modeling of phase function ϑ(t) (the sum of the phase and epoch) and periodic or quasiperiodic phase curves of tracers of the rotation (typically light curves), as the functions of ϑ(t). The phase function is con-nected with the generally variable rotational period P(t) through the basic relations (see Mikulášek et al. 2008b; Mikulášek 2016):
. ϑ = 1 P(t); ϑ(t) = Z t M0 dτ P(τ); θ(ϑ) = Z ϑ 0 P(ζ) dζ. (2)
The phase function ϑ(t) is a smooth, monotonically rising func-tion of time. The relafunc-tion for its inversion funcfunc-tion θ(ϑ) can be derived from the same basic differential equation. Using the in-version phase function, we can predict, for example, times of maxima or other important moments of the phase variations. 3.1. Model of light curves
The light curves, obtained at various times in the filters of dif-ferent effective wavelengths λeff from 130 to 753 nm, provide
2 IRAF is distributed by NOAO, which is operated by AURA, Inc.,
Table 2.Parameters of CU Vir ephemeris (Eq. (4)). M0 (HJD) 2 452 650.8991(6) P.0 [d] 0.520 716 59(8) P..0 4.9(2) × 10−10 P...0 [d−1] −1.762(11) × 10−12 P0 [d−2] −3.23(5) × 10−16
a massive amount of information about CU Vir rotation and its long-term variations. There is a general expectation (Paper I) that the shapes of CU Vir light curves strongly depend on the effec-tive wavelengths (see Fig. 1). Nevertheless, the careful inspec-tion revealed that all of the observed light curves can be satisfac-torily expressed as a linear combination of only two symmetric basic profiles with centers at phases ϑ0 jand half-widths dj:
F(λeff, ϑ) = 2 X j=1 Aj(λeff) ( exp " 1−cosh ∆ϕj dj !# − 2.29 dj ) ; where ∆ϕj=(ϑ − ϕ0 j) − round(ϑ − ϕ0 j), (3) where F(λeff, ϑ) is the model prediction of the difference of the magnitude with respect to its mean value as a function of the wavelength λeff and phase function ϑ, A1and A2are amplitudes depending on wavelengths, d1and d2are the half-widths of the basic profiles expressing their sizes, and ϕ01 and ϕ02 are the phases of their centers. This phenomenological model quanti-fies the fact known from our previous studies that the areas with abnormal spectral energy distribution of the flux on the surface are concentrated around just two prominent asymmetrically dis-tributed conglomerations (Paper I).
The phase of the center of the first spot was fixed at ϕ01 = 0.598, while the location of the center of secondary photometric spot (ϕ02 =0.3029(6)), as well as the basic profile half-widths, d1 = 0.1774(8) and d2 = 0.1491(6), were determined by iter-ativelly fitting observations. The zero phase corresponds to the light curve minimum in near UV and optical regions and to the maximum in far UV (see Fig. 1).
3.2. Model of phase function and period variations
The primary purpose of the proposed definition of the phase function model is finding as simple as possible ephemeris guar-anteeing the accuracy in the phase of at least 0.01 in 1970 – 2018. In this time interval, there were obtained 36 129 photo-metric observations or photophoto-metric measurements derived from UV spectra taken by IUE and HST. The data create 177 individ-ual light curves in 37 filters, covering substantial part of CU Vir electromagnetic spectrum. This volume of data is quite sufficient for approximation of the dimensionless phase curve ϑ(t) and its inversion function θ(ϑ) (with a time dimension) by the fourth order polynomial in the form of the Taylor decomposition: ϑ0= t−MP00; ϑ = ϑ0− 1 2! . P0ϑ20−3!1P0 .. P0ϑ30−4!1P20 ... P0ϑ40; θ(ϑ)= M0+ P0ϑ+2!1P0 . P0ϑ2+3!1P20 .. P0ϑ3+4!1P30 ... P0ϑ4; (4) ϕ =frac(ϑ); E =floor(ϑ); (5) P(t) P0+ P0 . P0ϑ0+2!1P20 .. P0ϑ20+3!1P30 ... P0ϑ30, (6)
where ϑ0is an auxiliary dimensionless quantity, M0is the origin of phase function, which was placed close to the weighted center of the observations, P0, . P0, .. P0,and ...
P0are the instantaneous pe-riod and its time derivatives up to third degree at the time t = M0,
Years 1970 1980 1990 2000 2010 2020 O-C pol4 [d] O-C lin [d] -0.01 0.00 0.01 -0.05 0.0 0.05 0.1 0.15 0.2 0.25 0.3
Fig. 2. Upper plot: O−Clinversus time in years. O is the moment of
the zero phase and Clin= M01+ P1× E. M01and P1are the
parame-ters of the linear approximation of O(E) behavior, E is the number of
rotational cycles elapsed from the initial epoch M01and P1is the mean
rotational period in the interval 1970–2018; M01=2 452 650.9048 and
P1 = 0.52070819 d. Nonlinearity of O−Clinis a result of variable
ro-tational period P. O−Clinis fitted by a fourth-order polynomial (solid
line). Bottom plot: The residuals O−Cpol4show that the model ensures
the accuracy of ephemeris 0.0025 d or 0.005 in phase. Optical photom-etry is denoted using yellow circles and UV spectrophotomphotom-etry derived from observed fluxes using green squares. Sizes of the symbols are in-versely proportional to the square root of the uncertainties of the deter-minations of O times derived from individual data sources.
ϕis the usual phase, and E is the epoch. We selected the Taylor expansion (4) as, contrary to the harmonic expansion (Krtiˇcka et al. 2017), it allowed us to directly calculate the phase and its in-version. Using relations in Eqs. (4) and (5) we can calculate the phase function ϑ, the epoch E, and the phase ϕ, for any HJD mo-ment t within the interval 1972 – 2020. Alternatively, knowing the particular phase function ϑ we can estimate corresponding time θ(ϑ). Changes of the instantaneous period P(t) = P(ϑ0) can be evaluated for any time t using relation (6).
3.3. Model solution and brief discussion of results
All 259 free parameters of our phenomenological model of CU Vir light curves and their corresponding uncertainties were determined together by robust regression (RR) as implemented in Mikulášek et al. (2003), which exploits the well-established procedures of the standard weighted least squares method and eliminates the influence of outliers. Instead of the usual χ2, we minimized the modified quantity χ2
r, defined as follows: ∆yi= yi− F(ti, γ), (7) χ2r =Pn i=1 ∆yi σri 2 ; where σri= σi exp 1 2 ∆yi 4 σi 4 , (8) χ2µ=1.06 χ2r nr−g; where nr =1.02 P σ−2 ri P σi −2, (9) δγk= q χ2µHkk, (10)
where ∆yi is the difference between the observed i-th measure-ment yiand the model prediction F(ti, γ), which is the function of the time of the measurement tiand the vector of the free model
Table 3.CU Vir parameters from spectroscopy. Kuschnig et al. 1999
Effective temperature Teff 13 000 K
Surface gravity log g (cgs) 4.0
Inclination i 30◦ Helium abundance −3.2 < εHe< −1 Silicon abundance −4.6 < εSi< −2.3 Chromium abundance −6.7 < εCr< −4.4 Iron abundance −5.5 < εFe < −3.5 Kochukhov et al. 2014
Effective temperature Teff 12 750 K
Surface gravity log g (cgs) 4.3
Radius R∗ 2.06 R⊙
Mass M 3.06 M⊙
Inclination i 46.5◦
Silicon abundance −5.7 < εSi< −2.3
Iron abundance −4.7 < εFe < −3.1
parameter γ, σiis the estimate of the uncertainty of determina-tion of the i-th measurement, while σriis a RR modified value of σi. The estimate of the common relative χ2µand the number of measurements without outliers nrare given by Eq. (9).
The formal uncertainties of the found parameters δγ were determined by the relation Eq. (10), where H is a covariant ma-trix of the system of equations. The most interesting parameters and their functions are listed in Table 2.
The comparison between observation and model predictions in Fig. 2 undoubtedly documents the high fidelity of the cho-sen model, which yields the phase function ephemeris describ-ing observations with the accuracy better than 0.005 in the inter-val 1972–2018. The derived period variations can be adequately fitted also by the harmonic polynomials instead of the Taylor ex-pansion (4) and interpreted as due to the torsional oscillations (Krtiˇcka et al. 2017).
4. Variations of the UV spectrum
4.1. Simulation of the spectral variability
The calculation of the model atmospheres and spectra is the same as described in Paper I. We used the TLUSTY code for the model atmosphere calculations (Hubeny 1988; Hubeny & Lanz 1992, 1995; Lanz & Hubeny 2003) with the atomic data taken from Lanz & Hubeny (2007). In particular, the atomic data for silicon and iron are based on Mendoza et al. (1995), Butler et al. (1993), Kurucz (1994), Nahar (1996), Nahar (1997), Bautista & Pradhan (1997), and Bautista (1996), and for other elements on Luo & Pradhan (1989), Fernley et al. (1999), Tully et al. (1990), Peach et al. (1988), Hibbert & Scott (1994), and Nahar & Prad-han (1993). We prepared our own ionic models for chromium (Cr ii–Cr v) using data taken from Kurucz (2009)3.
We used two different sets of surface abundance maps. Kuschnig et al. (1999) derived abundance maps of helium, mag-nesium, silicon, chromium, and iron. Kochukhov et al. (2014) derive abundance maps of silicon and iron only, but using an updated version of the inversion code that accounts also for the magnetic field. For each set of maps (from Kuschnig et al. (1999) and Kochukhov et al. (2014)) we adopted correspond-ing effective temperatures and surface gravities derived from spectroscopy (see Table 3) and assumed the range of abun-dances that covers values in individual maps as given in
Ta-3 http://kurucz.harvard.edu
Table 4.Individual abundances εHe, εSi, εCr, and εFeof the model grid.
He −2.0 −1.0
Si −4.75 −4.25 −3.75 −3.25 −2.75 −2.25
Cr −6.4 −5.9 −5.4 −4.9 −4.4
Fe −5.4 −4.9 −4.4 −3.9 −3.4 −3.1
ble 3. Here the abundances are given relative to hydrogen, that is, εel = log (Nel/NH). We neglected the influence of inhomo-geneous surface distribution of magnesium due to its low abun-dance. For each set of maps we used inclination that was derived from corresponding mapping (see Table 3). We used the solar abundance of other elements (Asplund et al. 2005).
For the calculation of synthetic spectra we used the SYN-SPEC code. The spectra were calculated for the same parame-ters (effective temperature, surface gravity, and chemical com-position) as the model atmospheres. We also took into account the same transitions (bound-bound and bound-free) as for the model atmosphere calculations. This is important for iron line transitions, for which many lines without experimental values significantly influence the spectral energy distribution. The re-maining line data are taken from the line lists available at the TLUSTY web page. We computed emergent specific intensities for 20 equidistantly spaced values of µ = cos θ, where θ is the angle between the normal to the surface and the line of sight.
The model atmospheres and the emergent specific intensi-ties I(λ, θ, εHe, εSi, εCr, εFe) were calculated for a four-parametric grid of helium, silicon, chromium, and iron abundances (see Ta-ble 4). The lowest abundances of individual elements are omitted from the grid. Our test showed that this restriction does not in-fluence the predicted light curves.
The radiative flux at the distance D from the star with radius R∗is (Hubeny & Mihalas 2014)
Fλ= R ∗ D 2 Z visible surface I(λ, θ, Ω) cos θ dΩ. (11)
The intensity I(λ, θ, Ω) at each surface point with spherical co-ordinates Ω is obtained by means of interpolation between the emergent specific intensities I(λ, θ, εHe, εSi, εCr, εFe) calculated from the grid of synthetic spectra (Table 4) taking into account the Doppler shifts due to the stellar rotation.
4.2. Comparison with the observed variations
We compared flux variations predicted using Eq. (11) with flux variations observed by HST/STIS for individual rotational phases ϕ. The predicted fluxes were scaled by the (R∗/D)2ratio derived in Paper I from the IUE spectra.
The fluxes calculated from the two sets of abundance maps show a good agreement with observed spectra for the spectral region around 1280 – 1475 Å (see Fig. 3) especially for the ro-tational phase ϕ ≈ 0, when the regions with low abundance of iron and silicon are visible. This spectral region is dominated by silicon bound-free and iron line transitions.
The two sets of abundance maps provide similar results for the 1494 – 1688 Å wavelength region, where the influence of sil-icon is weaker (see Fig. 4). The predicted fluxes nicely agree with observations for phases ϕ ≈ 0 and ϕ ≈ 0.2, while the pre-dicted fluxes are slightly larger than the observations for ϕ ≈ 0.4, ϕ ≈ 0.6, and ϕ ≈ 0.8. A detailed inspection of fluxes shows that
0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 1300 1350 1400 1450 Fλ [erg cm −2 s −1 Å −1 ] λ [Å] C I, Si II Si II Si II C II Ni II S I C I, Cr II P II HST/STIS od5y05010 predicted (old) ϕ=0.80 predicted (new) ϕ=0.80 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 2.5 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] C I, Si II Si II Si II C II Ni II S I C I, Cr II P II HST/STIS od5y51010 predicted (old) ϕ=0.04 predicted (new) ϕ=0.04 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] C I, Si II Si II Si II C II Ni II S I C I, Cr II P II HST/STIS od5y02010 predicted (old) ϕ=0.22 predicted (new) ϕ=0.22 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] C I, Si II Si II Si II C II Ni II S I C I, Cr II P II HST/STIS od5y03010 predicted (old) ϕ=0.37 predicted (new) ϕ=0.37 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] C I, Si II Si II Si II C II Ni II S I C I, Cr II P II HST/STIS od5y04010 predicted (old) ϕ=0.63 predicted (new) ϕ=0.63
Fig. 3.Predicted and observed (HST, black line) flux in selected phases for the wavelength range 1270 – 1480 Å. The gray line denotes spectra
calculated using Kuschnig et al. (1999) surface abundance distribution and blue line denotes spectra calculated using Kochukhov et al. (2014) surface abundance distribution. Individual strong lines and iron line blends are identified.
0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 1500 1550 1600 1650 Fλ [erg cm −2 s −1 Å −1 ] λ [Å] Si II Si II Si II C I, Si II, Fe II Fe II Fe II Al II Fe II Fe II C I HST/STIS od5y05020 predicted (old) ϕ=0.83 predicted (new) ϕ=0.83 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 2.5 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] Si II Si II Si II C I, Si II, Fe II Fe II Fe II Al II Fe II Fe II C I HST/STIS od5y51020 predicted (old) ϕ=0.06 predicted (new) ϕ=0.06 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] Si II Si II Si II C I, Si II, Fe II Fe II Fe II Al II Fe II Fe II C I HST/STIS od5y02020 predicted (old) ϕ=0.25 predicted (new) ϕ=0.25 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] Si II Si II Si II C I, Si II, Fe II Fe II Fe II Al II Fe II Fe II C I HST/STIS od5y03020 predicted (old) ϕ=0.40 predicted (new) ϕ=0.40 0 5.0 × 10−11 1.0 × 10−10 1.5 × 10−10 2.0 × 10−10 Fλ [erg cm −2 s −1 Å −1 ] Si II Si II Si II C I, Si II, Fe II Fe II Fe II Al II Fe II Fe II C I HST/STIS od5y04020 predicted (old) ϕ=0.66 predicted (new) ϕ=0.66
the new maps agree with observations even slightly better dur-ing the phases ϕ ≈ 0, ϕ ≈ 0.2, and ϕ ≈ 0.6 in the interval 1600 − 1650 Å. The remaining disagreement is likely caused by missing opacity due to some additional element(s). We tested the flux distribution calculated with enhanced abundance of light el-ements with Z < 30 and we have found that a missing opac-ity is possibly due to chromium. The predicted flux distribu-tion for ǫCr = −4 nicely matches the observations for ϕ ≈ 0.4. Chromium was mapped by Kuschnig et al. (1999), but new maps based on more detailed spectroscopy could possibly give higher chromium abundance in the spots.
We also tested new line data from the VALD database (Piskunov et al. 1995; Kupka et al. 1999; Ryabchikova 2015). This led to an improvement of the agreement in some specific lines, but caused disagreement in others. Consequently, part of the discrepancy between the predicted and observed spectra can be probably attributed to the imprecise line data.
In addition to the line variability of elements studied in opti-cal (silicon, chromium, and iron), the UV spectra also show car-bon line variability. Carcar-bon is roughly depleted by a factor of ten with respect to the solar value, consequently it is not expected to significantly affect the flux distribution. We also tested the pres-ence of lines of heavy elements, with atomic number Z ≤ 92, in the spectra of CU Vir. We used our original line list and the line list downloaded from the VALD database (Piskunov et al. 1995; Kupka et al. 1999; Ryabchikova 2015). We find no evidence for the presence of lines of elements having Z > 30 in the spectra of CU Vir.
5. Stellar wind of CU Vir
The explanation of CU Vir continuum radio emission by gy-rosynchrotron process requires a wind mass-loss rate on the or-der of 10−12M
⊙yr−1(Leto et al. 2006). However, wind models show that the radiative force is too weak to accelerate the wind for CU Vir’s effective temperature (Krtiˇcka 2014). To understand this inconsistency, we provide additional wind tests and search for the wind signatures in the CU Vir spectra.
We used our METUJE wind code (Krtiˇcka 2014) to test if the radiative force overcomes gravity in the envelope of CU Vir and to calculate the wind spectra. Our wind code solves the hydro-dynamic equations (equations of continuity, motion, and energy) in a stationary spherically symmetric stellar wind. The radiative transfer equation is solved in the comoving frame (CMF). The code allows us to treat the atmosphere and wind in a unified (global) manner (Krtiˇcka & Kubát 2017), but for the present purpose we modeled just the wind with the METUJE code, and we derived the base flux from the TLUSTY model atmo-sphere model with ǫHe = −1, ǫSi = −3.25, ǫCr = −5.4, and ǫFe = −3.1. To enable better comparison with the observed spec-tra, the TLUSTY flux in the regions of strong wind lines was re-placed by the flux predicted from inhomogeneous surface abun-dances for phase ϕ = 0.30.
For the wind tests, we assumed fixed wind density and veloc-ity and compared the radiative force with gravveloc-ity (Krtiˇcka 2014). We tested mass-loss rates in the range of 10−14− 10−10M
⊙yr−1 for mass-fractions of the heavy elements Z relative to the solar value Z⊙ in the range Z = Z⊙− 103Z
⊙ scaling abundances of all elements heavier than helium by the same value. The radia-tive force is typically one or two orders of magnitude lower than the gravitational acceleration (in absolute values). The radiative force overcomes gravity only for the most metal rich model with Z = 103Z⊙, which is higher than the fraction of silicon and iron found in metal rich regions on the CU Vir surface (see Table 3).
0.0 0.5 1.0 1.5 2.0 2.5 1320 1330 1340 1350 1360 Fλ [10 −10 erg cm −2 s −1 Å −1 ] λ [Å] CII 4×10−12 M⊙ yr−1 3×10−11 M⊙ yr−1 od5y03010 no wind 0.5 1.0 1.5 2.0 2.5 3.0 1840 1850 1860 1870 Fλ [10 −10 erg cm −2 s −1 Å −1 ] λ [Å] AlIII AlIII 4×10−12 M⊙ yr−1 3×10−11 M⊙ yr−1 SWP 3866 no wind 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1880 1890 1900 1910 Fλ [10 −10 erg cm −2 s −1 Å −1 ] λ [Å] FeIII 4×10−12 M⊙ yr−1 3×10−11 M⊙ yr−1 SWP 3866 no wind
Fig. 5.Predicted wind spectra for two values of mass-loss rates (red
lines) in comparison with spectra without wind (blue line) and observed spectra (gray line).
Consequently, we find no wind in CU Vir from our theoretical models. This is consistent with results of Babel (1996), who also found no wind for stellar parameters corresponding to CU Vir. A weak, purely metallic wind with M ≈ 10. −16M
⊙yr−1 is still possible for such low-luminosity stars (Babel 1995).
Spectral lines originating in the wind have in general com-plex line profiles, which depend on the wind mass-loss rate, ve-locity law, and ionization balance. Especially at low wind densi-ties, the wind line profiles could be hidden in blends of numerous
UV lines. Therefore, to determine which wind lines could possi-bly be found in the observations, we used our METUJE code to predict the wind spectra. We assumed Z = 102Z
⊙, which roughly corresponds to the most silicon and iron rich surface layers and artificially multiplied the radiative force by a factor of 3–10 to get wind model to converge with different wind mass-loss rates. Below we discuss further two representative wind models with a mass-loss rate M =. 4 × 10−12M⊙yr−1 and terminal velocity v∞=1010 km s−1and a model withM =. 3 × 10−11M
⊙yr−1and v∞=1850 km s−1.
We find that the strongest wind features appear in the C ii lines at 1335 Å and 1336 Å and in the Al iii lines at 1855 Å and 1863 Å (Fig. 5). Aluminum lines are predicted to show strong absorption and emission in P Cygni profiles. The absorption is weaker in the model with lower mass-loss rate and less blue-shifted as a result of lower wind terminal velocity. The carbon lines show P Cygni profiles with slightly extended absorption and show emission only for the highest mass-loss rates consid-ered. These lines become weaker close to the blue edge of the P Cygni line profile due to C ii ionization. There are no such features in the observed spectra of CU Vir. If the assumed abun-dances are correct, this would limit the CU Vir mass-loss rate toM .. 10−12M
⊙yr−1, below the value required to explain the radio emission (Leto et al. 2006). On the other hand, the photo-spheric components of C and Al lines show that these elements are likely underabundant (similarly to carbon on the surface of σ Ori E, Oksala et al. 2015). In such a case the wind lines of these elements would not be present in the spectra and the im-posed wind limit should be higher.
Therefore, we concentrated on the wind lines of silicon and iron, the two elements which are overabundant on the surface of CU Vir. The 1394 Å and 1403 Å lines of Si iv, which might be relatively strong in the spectra of stars with slightly higher ef-fective temperature (Krtiˇcka 2014), do not appear in the CU Vir spectra due to silicon recombination. Therefore, the strongest limit to the mass-loss rate comes from the absence of Fe iii 1895 Å wind line in Fig. 5, which givesM .. 10−11M⊙yr−1.
Spectra in Fig. 5 are plotted for a particular phase ϕ ≈ 0.3. In magnetic stars, the wind properties depend on the tilt of the magnetic field (e.g., ud-Doula et al. 2009), therefore, the wind line profiles show rotational variability (Bjorkman et al. 1994; Marcolino et al. 2013; Nazé et al. 2015). We tested the existence of the wind also in other phases with similar conclusions as for the phase ϕ ≈ 0.3. Consequently, we conclude that the presence of the stellar wind in CU Vir can not be proven even from our spectra with the highest quality. This corresponds to observation of very weak wind lines in early-type magnetic stars (Oskinova et al. 2011). These lines give the mass-loss rate on the order of 10−11− 10−10M
⊙yr−1, but for stars whose luminosity is nearly two magnitudes higher. Given a strong dependence of mass-loss rate on luminosity, the upper limit of the CU Vir mass-loss rate is not surprising.
There are additional possible wind indicators in the wave-length region between the Lyman jump and Lyα line. The 1086 Å N ii line is predicted to show nice P Cygni line profile, but it is located in the region where the model flux is roughly one order of magnitude lower than the flux in the 1300–1400 Å region. The lines 1176 Å C iii and 1206 Å Si iii are located in the wavelength region covered by the IUE observations, but the ob-served flux is rather noisy. In any case, the obob-served spectra in the region of 1206 Å Si iii are consistent with the 10−11M
⊙yr−1 limit of the mass-loss rate.
Table 5.Lines searched in CU Vir spectra for auroral emission.
Ion Lines [Å] He ii 1640 C i 1330, 1561, 1657 C ii 1335 O i 1302, 1305, 1306, 1356, 1359 Si i 1556 – 1675 Si ii 1305, 1309, 1527, 1533 P i 1381 P ii 1533, 1536, 1542, 1543, 1544 S i 1283 – 1475 Cl i 1347, 1352 Ti iii 1282 – 1300 Fe ii 1559 – 1686 Co ii 1448, 1456, 1466. 1473, 1509, 1548 Ni ii 1317, 1335, 1370, 1411 Cu ii 1359
CU Vir has relatively strong magnetic field, which may af-fect the calculation of the radiative force and wind line profiles (e.g., Shenar et al. 2017). The wind lines originate in the mag-netosphere with a complex structure leading to the dependence of wind line profiles on phase and inclination (e.g., Marcolino et al. 2013). The plasma effects become important in the wind at low densities and the wind behaves as a multicomponent flow (Krtiˇcka & Kubát 2002). Moreover, at low densities the shock cooling length is comparable to the radial wind scale, possibly causing weak wind line profiles (Cohen et al. 2008; Krtiˇcka & Kubát 2009; Lucy 2012). We tested the inclusion of complete photoionization cross-sections for Si ii – Si iii (with autoioniza-tion resonances, Butler et al. 1993). This has not lead to a signif-icant increase of the radiative force, but there may still be some elements missing in our list (Krtiˇcka & Kubát 2009) that are overabundant on CU Vir’s surface and may drive a wind. More-over, wind inhomogeneities (clumping) affect wind ionization state and wind line profiles (Sundqvist et al. 2010; Šurlan et al. 2012). Although Oskinova et al. (2011) finds no significant dif-ferences in the spectra of clumped and smooth stellar wind for their particular model of B star, there might still be significant effects of clumping for other stellar parameters. Therefore, there still might be possibilities to launch stellar wind in CU Vir that does not show any signatures in UV spectra, but at the moment there is no theoretical nor observational support for the existence of the stellar wind in CU Vir.
6. Search for auroral lines
The radio emission in CU Vir originates due to processes resem-bling auroral activity in Earth and giant planets (Trigilio et al. 2011). Therefore, we searched for auroral lines in the UV spec-tra of CU Vir. Because the auroral lines originate from the rigidly rotating magnetosphere, we expect these lines to be broadened by at least vrotsin i = 145 km s−1, which corresponds to the pro-jected equatorial rotational velocity (Kochukhov et al. 2014). Moreover, the auroral lines would likely show rotational vari-ability as a result of complex structure of the magnetosphere.
The planetary auroral emission comprises molecular lines (e.g., Soret et al. 2016; Gustin et al. 2017), which are not ex-pected in CU Vir due to its high temperature. We searched for the auroral emission of neutral oxygen lines given in Table 5, which are detected in planetary magnetospheres (e.g., Molyneux et al. 2014; Soret et al. 2016). The lower level of all these lines
−14.5 −14.0 −13.5 −13.0 −12.5 −12.0 −11.5 −11.0 −10.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 vrad [km s −1 ] phase ϕ O I 1302 Å Si II 1304 Å C II 1335 Å C II 1336 Å Si II 1527 Å Fe II 1608 Å Al II 1671 Å
Fig. 6.Variation of the radial velocity shift of the interstellar lines with
phase. Derived from δλ parameter of the fit (12) using the Doppler law. corresponds to the ground state. We find no auroral lines of neu-tral ions. This is not surprising, as our wind models indicate that the magnetosphere is dominated by singly and doubly ionized elements.
Therefore, we also searched for the auroral emission in lines whose lower level corresponds to the ground state of singly and doubly ionized elements (see Table 5). We did not find any emission line profiles that can be attributed to the circumstel-lar medium, either. However, this does not necessary mean that there are no such lines present in the available spectra. Given the complexity and variability of photospheric spectra, the auroral lines may remain overlooked.
Some hot white dwarfs show ultra-high excitation absorp-tion lines in their spectra (e.g., Werner et al. 1995; Dreizler et al. 1995; Reindl et al. 2019). These lines possibly originate in shock-heated magnetospheres of white dwarfs. Such a process can also appear in magnetic main-sequence stars. We searched for these lines in the optical spectra of CU Vir, but we have not found any.
7. Lines of interstellar medium
HST/STIS spectra of CU Vir show several interstellar lines, which are missing in Figs. 3 and 4 due to the application of me-dian filter. We studied the variability of interstellar lines in the original spectra downloaded from MAST archive. For this pur-pose we fitted the individual interstellar lines by
F(λ) = (F0+ F1λ) exp ( −s exp " − λ − λ0− δλ d 2#) , (12)
which is a solution of the radiative transfer equation in a uni-form medium with Gaussian line absorption. Parameters F0and F1account for the stellar continuum, λ0is the laboratory wave-length of a given line, and s, δλ, and d are parameters of the fit.
We identify individual interstellar lines using the list pro-vided by Cox (2000). We fitted them by line profile function Eq. (12) and searched for the phase variability of the line param-eters. We find phase variability of the line shift δλ (see Fig. 6),
Table 6.Parameters of the fit Eq. (12) of individual interstellar lines.
Line δλ[mÅ] d[mÅ] O i 1302 Å −59.9 ± 0.8 23.8 ± 1.4 Si ii 1304 Å −53.3 ± 0.8 19.2 ± 1.1 C ii 1335 Å −57.3 ± 0.7 28.0 ± 0.7 C ii 1336 Å −55.5 ± 0.7 13.6 ± 0.4 Si ii 1527 Å −69.4 ± 1.2 24.4 ± 0.7 Fe ii 1608 Å −65.6 ± 1.6 15.4 ± 0.5 Al ii 1671 Å −71.7 ± 1.7 22.6 ± 0.5
which is correlated with line width parameter d in both STIS bands.
It is tempting to attribute these variations to circumstellar clouds that amplify the interstellar absorption. The centrifugally supported circumstellar clouds can exist above the radius where the centrifugal force overcomes gravity r = h
GMP2/4π2i1/3 (Townsend & Owocki 2005), which for the stellar parameters given in Table 3 gives r = 1.9 R∗. This is at odds with es-timated temperature of the clouds. The Si ii 1533 Å line with lower-level excitation energy 0.036 eV is not present in the spec-trum, while C ii 1336 Å line with lower-level excitation energy 0.008 eV is clearly visible. This implies the temperature of ab-sorbing medium on the order of 10 K, which cannot be achieved in a close proximity of the star. Moreover, the expected rota-tional line broadening due to rigidly rotating centrifugal magne-tosphere, which is at least equal to the surface rotational velocity vrotsin i = 145 km s−1 (Kochukhov et al. 2014), is an order of magnitude higher than the observed broadening of interstellar lines. The difference between the shift estimated from the spec-tra centered at 1380 Å and specspec-tra centered at 1598 Å around the phase ϕ ≈ 0.8 (Fig. 6) is comparable to the uncertainty of δλ. Fi-nally, the unsaturated C ii 1336 Å line shows the same variability as saturated lines implying comparable absorption due to both the interstellar medium and to the putative circumstellar cloud. Consequently, we conclude that the line variability in Fig. 6 does not originate in the centrifugal magnetosphere and that it is likely generated further out from the star.
We also tested the possibility that the interstellar line vari-ability is a result of a constant circumstellar absorption acting on variable flux. For this purpose we used simulated spectra at-tenuated by circumstellar line absorption and fitted the result-ing spectra by Eq. (12). We detected only order of magnitude smaller variations than those derived from observations. Conse-quently, the observed variations of the interstellar medium lines are most likely only of instrumental origin. Although the STIS spectrograph provides subpixel wavelength stability (i.e., lead-ing to lower changes than that seen in Fig. 6, Riley et al. 2018), subsequent processing of variable spectra likely leads to larger differences. We therefore simply averaged the radial velocities inferred from Table 6 to get the mean radial velocity of the inter-stellar medium of −12.9 ± 0.4 kms−1. Because CU Vir is located close to the rim of the Spica Nebula, which results from the in-teraction of the Local Bubble with another interstellar bubble (Choi et al. 2013), the interstellar lines in CU Vir spectra may be connected with these structures.
8. Discussion: Tracing the wind
The upper limit for the wind mass-loss rate 10−12M
⊙yr−1is in tension with the mass-loss rate on the order of 10−12M
re-quired to explain the CU Vir radio emission (Leto et al. 2006). This estimate was derived assuming the balance between the ram pressure of the wind and the plasma pressure in the inner mag-netosphere. On the other hand, leaving this requirement and as-suming instead that the magnetospheric plasma is in hydrostatic equilibrium (Townsend & Owocki 2005) allows for much lower wind mass-loss rate required to feed the magnetosphere. Within such a model, even the pure metallic wind predicted by Babel (1996) might be strong enough to power the radio emission.
In contrast, even relatively strong wind is consistent with the angular momentum loss via the magnetized stellar wind. This mechanism affects the rotational velocities of early-B stars (Shultz et al. 2017) and should be present also in late-B stars with winds. AssumingM =. 10−12M⊙yr−1, a typical wind termi-nal velocity v∞ = 1000 km s−1, dipolar magnetic field strength of CU Vir Bp=3 kG (Kochukhov et al. 2014), and angular mo-mentum constant k = 0.08 as derived from MESA models (Pax-ton et al. 2011, 2013, see Krtiˇcka et al. 2017 for details) we de-rive from Eq. (25) of ud-Doula et al. (2009) the spin-down time 1.4×108yr, which is consistent with an estimated age ≤ 100 Myr of CU Vir (Kochukhov et al. 2014).
The stellar wind also likely powers X-ray emission of CU Vir (Robrade et al. 2018). Assuming full conversion of wind ki-netic energy to X-rays, then with wind terminal velocity v∞ = 1000 km s−1, a mass-loss rate 10−13M
⊙yr−1is required to power the X-ray luminosity LX=3 × 1028erg s−1derived from the ob-servations. This mass-loss rate is below the upper limit derived here.
It is unclear what drives the supposed torsional oscillations in CU Vir. The properties of the corresponding energy source can be estimated from the total energy of these oscillations, which is given by the kinetic energy density of oscillatory motion inte-grated over the whole stellar volume,
Eto=4π Z R∗
0 r21
2ρδ32dr, (13)
where δ3 is the velocity amplitude of the oscillations, which is connected with the amplitude of the angular frequency by δ3 = rδΩ. The surface value of the amplitude of the angular frequency δΩ∗can be derived from the harmonic fit of the period variability P(t) = P0+ Asin [2 π (t − Θ0) /Π] (Krtiˇcka et al. 2017) as δΩ∗≈ 2πA/P2
0. Here A and Π are the amplitude and length of the cycle of rotational period evolution. From this, the total energy of the torsional oscillations is Eto=8π3A 2 P40 Z R∗ 0 r 4ρ δΩ δΩ∗ !2 dr. (14)
The energy can be conveniently rewritten using the angular mo-mentum constant k, and assuming that δΩ does not depend on radius one can get an estimate Eto=2π2kMR2A2/P40.
To derive a more precise estimate of the total energy of the torsional oscillations, we used the stellar density distribution from the discussed MESA stellar evolutionary model. We as-sumed that the amplitude of δΩ is proportional to the amplitude of u1variable for time t = 10 Π of torsional oscillation simula-tions (Krtiˇcka et al. 2017, Fig. 1). The selection of a particular time t does not have a significant effect on estimated value of Eto. We scaled the numerical solution for u1using the observed vari-ations of rotational period at the stellar surface. These assump-tions yield Eto = 5 × 1037erg, which is just about 5 × 10−7 of the total energy of X-rays emitted during the whole CU Vir life-time (assuming constant LXand an upper limit of CU Vir age,
100 Myr, Kochukhov et al. 2014). Consequently, stellar wind, which presumably powers the X-ray emission, provides a con-venient energy source also for the torsional oscillations.
The continuous wind leakage from the magnetosphere is likely not the mechanism that drives the oscillations, but a sud-den energy release during the reconnection event that opens up the magnetosphere (Townsend & Owocki 2005) might be more likely. Such events are probably very rare, because the corresponding breakout time is about 105yr as estimated from Eq. (A8) of Townsend & Owocki (2005) for CU Vir parameters.
9. Conclusions
We analyzed the HST/STIS spectra of the enigmatic chemically peculiar star CU Vir. This is the first discovered main-sequence star showing coherent directive radio emission (Trigilio et al. 2000). The existence of such radio emission requires wind with mass-loss rate on the order of 10−12M
⊙yr−1 as a source of free electrons (Leto et al. 2006). However, the effective tem-perature of CU Vir is below the limit of homogeneous winds Teff ≈ 15 000 K (Krtiˇcka 2014). Our analysis of UV spectra of the star has not revealed any wind signatures and puts the upper limit of CU Vir mass-loss rate at about 10−12M
⊙yr−1. Although the physics of low density winds is complex and there are rea-sons for even stronger winds to remain hidden from UV analy-sis, we argue that even weaker inhomogeneous (metallic) wind of Babel (1996) may be a reasonable source of free electrons to power the radio and X-ray emission of CU Vir.
We searched for other signatures of magnetospheric plasma including auroral emission lines and deep absorption lines. How-ever, we have not found any signatures that can be attributed to magnetospheric plasma.
CU Vir shows long-term rotational period variations (Pyper et al. 1998; Mikulášek et al. 2011). We analyzed these varia-tions using available UV observavaria-tions supplemented with our own and archival optical photometric data. We concluded that the data from optical and UV domains show the same long-term evolution of the rotational period. This supports the picture that the UV and optical variations are related and that the structures leading to these variations are rigidly confined to the stellar sur-face.
We modeled the UV flux variability assuming its origin in the surface abundance spots, in which the flux redistribution due to bound-bound and bound-free processes takes place. We show that the updated abundance maps of Kochukhov et al. (2014) provide improved flux distributions that agree better with obser-vations mainly around 1600 Å.
Acknowledgements. This research was supported by grants GA ˇCR 16-01116S
and in final phases by GA ˇCR 18-05665S. GWH acknowledges long-term sup-port from NASA, NSF, and the Tennessee State University Center of Excellence, as well as NASA grant HST-GO-14737.002-A. OK acknowledges support by the Knut and Alice Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board. AP acknowledges the support from the National Science Centre grant no. 2016/21/B/ST9/01126. This research was partly based on the IUE data derived from the INES database using the SPLAT package.
References
Alecian, G., Stift, M. J., & Dorfi, E. A. 2011, MNRAS, 418, 986
Asplund, M., Grevesse, N., & Sauval, A. J. 2005, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, ASP Conf. Ser. 336, eds. T. G. Barnes III, F. N. Bash (San Francisco: ASP), 25
Babel, J. 1995, A&A, 301, 823 Babel, J. 1996, A&A, 309, 86 Bautista, M. A. 1996, A&AS, 119, 105
Bautista, M. A., & Pradhan, A. K. 1997, A&AS, 126, 365
Bjorkman, J. E., Ignace, R., Tripp, T. M., & Cassinelli, J. P. 1994, ApJ, 435, 416 Butler, K., Mendoza, C., & Zeippen, C. J. 1993, J. Phys. B, 26, 4409
Choi, Y.-J., Min, K.-W., Seon, K.-I., et al. 2013, ApJ, 774, 34
Cohen D. H., Kuhn M. A., Gagné M., Jensen E. L. N., Miller N. A., 2008, MN-RAS, 386, 1855
Cox, A. N., ed., 2000, Astrophysical Quantities (New York: AIP Press) Das, B., Chandra, P., & Wade, G. A. 2018, MNRAS, 474, L61
Draper, P. W. 2004, SPLAT: A Spectral Analysis Tool, Starlink User Note 243 (University of Durham)
Dreizler, S., Heber, U., Napiwotzki, R., & Hagen, H. J. 1995, A&A, 303, L53 Eyles, C. J., Simnett, G. M., Cooke, M. P., et al. 2003, Sol. Phys., 217, 319 Fernley, J. A., Hibbert, A., Kingston, A. E., & Seaton, M. J. 1999, J. Phys. B, 32,
5507
Gustin, J., Grodent, D., Radioti, A., et al. 2017, Icarus, 284, 264 Henry, G. W. 1999 PASP, 111, 845
Hess, S. L. G., & Zarka, P. 2011, A&A, 531, A29 Hibbert, A., & Scott, M. P. 1994, J. Phys. B, 27, 1315
Hick, P., Buffington, A., & Jackson, B. V. 2007, in Proc. SPIE, Vol. 6689, Solar Physics and Space Weather Instrumentation II, 66890C
Hubeny, I. 1988, Comput. Phys. Commun., 52, 103 Hubeny, I., & Lanz, T. 1992, A&A, 262, 501 Hubeny, I., & Lanz, T. 1995, ApJ, 439, 875
Hubeny, I., & Mihalas, D., 2014, Theory of Stellar Atmospheres (Princeton Uni-versity Press, Princeton)
Jackson, B. V., Buffington, A., Hick, P. P., et al. 2004, Sol. Phys., 225, 177 Kochukhov, O., Lüftinger, T., Neiner, C., & Alecian, E. 2014, A&A, 565, A83 Kodaira, K. 1973, A&A, 26, 385
Krtiˇcka, J. 2014, A&A, 564, A70
Krtiˇcka, J., & Kubát, J. 2002, A&A, 388, 531 Krtiˇcka, J., & Kubát, J. 2009, MNRAS, 394, 2065 Krtiˇcka, J., & Kubát, J. 2017, A&A, 606, A31
Krtiˇcka, J., Mikulášek, Z., Lüftinger, T. et al. 2012, A&A, 537, A1 (Paper I) Krtiˇcka, J., Mikulášek, Z., Henry, G. W., Kurfürst, P., & Karlický, M. 2017,
MNRAS, 464, 933
Krtiˇcka, J., Mikulášek, Z., Henry, G. W., et al. 2009, A&A, 499, 567
Kupka, F., Piskunov, N. E., Ryabchikova, T. A., Stempels, H. C., & Weiss, W. W. 1999, A&AS, 138, 119
Kurucz, R. L. 1994, Kurucz CD-ROM 22, Atomic Data for Fe and Ni (Cam-bridge: SAO)
Kuschnig, R., Ryabchikova, T. A., Piskunov, N. E., Weiss, W. W., & Gelbmann, M. J. 1999, A&A, 348, 924
Lanz, T., Artru, M.-C., Le Dourneuf, M., & Hubeny, I. 1996, A&A, 309, 218 Lanz, T., & Hubeny, I. 2003, ApJS, 146, 417
Lanz, T., & Hubeny, I. 2007, ApJS, 169, 83
Lenc, E., Murphy, T., Lynch, C. R., Kaplan, D. L., & Zhang, S. N. 2018, MN-RAS, 478, 2835
Leto, P., Trigilio, C., Buemi, C. S., Umana, G., & Leone, F. 2006, A&A, 458, 831
Leto, P., Trigilio, C., Buemi, C. S., et al. 2016, MNRAS, 459, 1159 Leto, P., Trigilio, C., Buemi, C. S., et al. 2017, MNRAS, 469, 1949 Leto, P., Trigilio, C., Oskinova, L. M., et al. 2019, MNRAS, 482, L4 Lo, K. K., Bray, J. D., Hobbs, G., et al. 2012, MNRAS, 421, 3316 Lüftinger, T., Kochukhov, O., Ryabchikova, T., et al. 2010, A&A, 509, A71 Lucy L. B. 2012, A&A, 544, A120
Luo, D., & Pradhan, A. K., 1989, J. Phys. B, 22, 3377
Marcolino, W. L. F., Bouret, J.-C., Sundqvist, J. O., et al. 2013, MNRAS, 431, 2253
Mendoza, C., Eissner, W., Le Dourneuf, M., & Zeippen, C. J. 1995, J. Phys. B, 28, 3485
Mestel L., & Weiss N. O., 1987, MNRAS, 226, 123
Michaud, G. 2004, in The A-Star Puzzle, IAU Symposium No. 224, eds. J. Zverko, J. Žižˇnovský, S. J. Adelman, & W. W. Weiss (Cambridge: Cambridge Univ. Press), 173
Mikulášek, Z., Krtiˇcka, J., Henry, G. W., et al. 2011, A&A, 534, L5
Mikulášek, Z. 2016, Contributions of the Astronomical Observatory Skalnaté Pleso, 46, 95
Mikulášek, Z., Žižˇnovský, J., Zverko, J. & Polosukhina, N. S. 2003, Contribu-tions of the Astronomical Observatory Skalnaté Pleso, 33, 29
Mikulášek, Z., Krtiˇcka, J., Henry, G. W. et al. 2008b, A&A, 485, 585
Molyneux, P. M., Bannister, N. P., Bunce, E. J., et al. 2014, Planet. Space Sci., 103, 291
Molnar, M. R. 1973, ApJ, 179, 527
Molnar, M. R., & Wu C.-C. 1978, A&A, 63, 335 Nahar, S. N. 1996, Phys. Rev. A, 53, 1545 Nahar, S. N. 1997, Phys. Rev. A, 55, 1980
Nahar, S. N., & Pradhan, A. K. 1993, J. Phys. B 26, 1109
Nazé, Y., Sundqvist, J. O., Fullerton, A. W., et al. 2015, MNRAS, 452, 2641 Oksala, M. E., Kochukhov, O., Krtiˇcka, J., et al. 2015, MNRAS, 451, 2015 Oskinova, L. M., Todt, H., Ignace, R. et al. 2011, MNRAS, 416, 1456
Owocki, S. P., & Puls, J., 2002 ApJ, 568, 965
Paxton B., Bildsten, L., Dotter A., et al., 2011, ApJS, 192, 3 Paxton B., Cantiello, M., Arras P., et al., 2013, ApJS, 208, 4 Peach, G., Saraph, H. E., & Seaton, M. J. 1988, J. Phys. B, 21, 3669 Peterson, D. M. 1970, ApJ, 161, 685
Piskunov, N. E., Kupka, F., Ryabchikova, T. A., Weiss, W. W., & Jeffery, C. S. 1995, A&AS, 112, 525
Prvák M., Liška J., Krtiˇcka J., Mikulášek Z., Lüftinger, T., 2015, A&A, 584, A17 Pyper, D. M., Ryabchikova, T., Malanushenko, V., et al. 1998, A&A, 339, 822 Pyper D. M., Stevens, I. R., & Adelman S. J., 2013, MNRAS, 431, 2106 Ravi, V., Hobbs, G., Wickramasinghe, D., et al. 2010, MNRAS, 408, L99 Reindl, N., Bainbridge, M., Przybilla, N., et al. 2019, MNRAS, 482, L93 Riley, A., et al. 2018, STIS Instrument Handbook, Version 17.0, (Baltimore:
STScI)
Robrade, J., Oskinova, L. M., Schmitt, J. H. M. M., Leto, P., & Trigilio, C. 2018, A&A, 619, A33
Ryabchikova, T., Piskunov, N., Kurucz, R.L., et al., 2015, Physics Scripta, 90, 054005
Shenar, T., Oskinova, L. M., Järvinen, S. P., et al. 2017, A&A, 606, A91 Shultz, M., Wade, G., Rivinius, T., et al. 2017, The Lives and Death-Throes of
Massive Stars, 329, 126
Škoda, P. 2008, Astronomical Spectroscopy and Virtual Observatory, eds. M. Guainazzi and P. Osuna (ESA), 97
Sokolov, N. A. 2000, A&A, 353, 707
Soret, L., Gérard, J.-C., Libert, L., et al. 2016, Icarus, 264, 398 Sundqvist, J. O., Puls, J., & Feldmeier, A. 2010, A&A, 510, A11
Šurlan B., Hamann W.-R., Kubát J., Oskinova L., Feldmeier A., 2012, A&A 541, A37
Townsend, R. H. D., & Owocki, S. P. 2005, MNRAS, 357, 251
Trigilio, C., Leto, P., Leone, F., Umana, G., & Buemi, C. S. 2000, A&A, 362, 281
Trigilio, C., Leto, P., Umana, G., Buemi, C. S., & Leone, F. 2008, MNRAS, 384, 1437
Trigilio, C., Leto, P., Umana, G., Buemi, C. S., & Leone, F. 2011, ApJ, 739, L10 Tully, J. A., Seaton, M. J., & Berrington, K. A. 1990, J. Phys. B, 23, 3811 ud-Doula A., Owocki S. P., & Townsend R. H. D. 2009, MNRAS, 392, 1022 Votruba, V., Feldmeier, A., Kubát, J., Rätzel, D. 2007, A&A, 474, 549 Werner, K., Dreizler, S., Heber, U., et al. 1995, A&A, 293, L75
